论文标题
在强烈的pi型环上与不合时宜
On Strongly pi-Regular Rings with Involution
论文作者
论文摘要
回想一下，如果对于每个r中的每个a，都有一个正整数n，则根据a，将一个r r称为强烈的pi-groumar。在本文中，我们进一步研究了强烈的PI-Star定期环的概念，该环是强烈的pi型环形环的星星，最初是由Cui-wang在J. Korean Math中引入的。 Soc。 （2015）。我们还建立了这些环的各种特性，并在（强）pi-pribolity和contion方面给出了几种新的特征。由于代数Colloq中的Cui-Yin，我们的结果也大大扩展了该主题的最新结果。 （2018年）被证明是PI-Star-ward-trigarlar环，并且由于J. Algebra Appl中的Cui-Danchev。 （2020年）被证明是恒星周期性的环。
Recall that a ring R is called strongly pi-regular if, for every a in R, there is a positive integer n, depending on a, such that a^n belongs to the intersection of a^{n+1}R and Ra^{n+1}. In this paper we give a further study of the notion of a strongly pi-star-regular ring, which is the star-version of strongly pi-regular rings and which was originally introduced by Cui-Wang in J. Korean Math. Soc. (2015). We also establish various properties of these rings and give several new characterizations in terms of (strong) pi-regularity and involution. Our results also considerably extend recent ones in the subject due to Cui-Yin in Algebra Colloq. (2018) proved for pi-star-regular rings and due to Cui-Danchev in J. Algebra Appl. (2020) proved for star-periodic rings.
